Prove that The lines joining the origin to the points of intersection of the line `3x-2y =1` and the curve `3x^2 + 5xy -3y^2+2x +3y= 0`, are are at right angles.

The lines joining the origin to the points of intersection of 2x^2 + 3xy -4x +1 = 0 and 3x + y=.1 given by

Find the equation to the pair of straight lines joining the origin to the intersections oi the straight line y=mx + c and the curve x^2 + y^2=a^2 . Prove that they are at right angles if 2c^2=a^2(1+m^2) .

Prove that the angle between the lines joining the origin to the points of intersection of the straight line y=3x+2 with the curve x^2+2x y+3y^2+4x+8y-11=0 is tan^(-1)((2sqrt(2))/3)

If the straight lines joining origin to the points of intersection of the line x+y=1 with the curve x^2+y^2 +x-2y -m =0 are perpendicular to each other , then the value of m should be

If the lines joining the origin to the intersection of the line y=nx+2 and the curve x^2+y^2=1 are at right angles, then the value of n^2 is

Find the equations of the straight lines joining the origin to the points of intersection of x^2+y^2-4x-2y=0 and x^2+y^2-2x-4y=4 .

The pair of lines joining origin to the points of intersection of, the two curves ax^2+2hxy + by^2+2gx = 0 and a^'x^2 +2h^'xy + b^'y^2 + 2g^'x = 0 will be at right angles, if

The lines joining the origin to the point of intersection of x^2+y^2+2gx+c=0 and x^2+y^2+2fy-c=0 are at right angles if

The distance of the point of intersection of the lines 2 x- 3y + 5 = 0 and 3x + 4y =0 from the line 5x-2y =0 is

The equation of the line joining the point {3, 5) to the point of intersection of the lines 4x + y - 1 = 0 and 7x - 3y - 35 = 0 is equidistant from the points (0,0) and (8,34) .